Abstract
Let [Formula: see text] denote the degree [Formula: see text] dilation of a point set [Formula: see text] in the domain of plane geometric spanners. If [Formula: see text] is the infinite square lattice, it is shown that [Formula: see text] and [Formula: see text]. If [Formula: see text] is the infinite hexagonal lattice, it is shown that [Formula: see text] and [Formula: see text]. All our constructions are planar lattice tilings constrained to degree [Formula: see text] or [Formula: see text].
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